Question: Simplify the following expression: $ a = \dfrac{2}{9} + \dfrac{10p}{p + 8} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{p + 8}{p + 8}$ $ \dfrac{2}{9} \times \dfrac{p + 8}{p + 8} = \dfrac{2p + 16}{9p + 72} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{10p}{p + 8} \times \dfrac{9}{9} = \dfrac{90p}{9p + 72} $ Therefore $ a = \dfrac{2p + 16}{9p + 72} + \dfrac{90p}{9p + 72} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{2p + 16 + 90p}{9p + 72} $ $a = \dfrac{92p + 16}{9p + 72}$